It is of central importance in a gas turbine to determine the temperature distribution in the hot gas flow at the turbine outlet, since the efficiency of the overall gas turbine is influenced by this temperature distribution. In particular, this temperature distribution is critical for improving the design of the turbine and for controlling the turbine operation. In particular in relation to turbine control, it is known that the time constant of the TOT measured value pick-up (TOT=Turbine Outlet Temperature), which is currently in use and operates using thermocouples, is greater than one second (approximately 3 s), while the time constant of the turbine blades is below one second. This results in the risk of damage to the first turbine stages since the thermocouples cannot detect a thermal overload with the required speed. Furthermore, in the case of measured value pick-ups based on thermocouples, any attempt at increasing the time response results, without exception, in a reduction in the service life.